One doesn't have to be a Mayan to believe that 21.12.2012 represents a numerological end of an era. Apocalyptic visions stem from reading the Mesoamerican long count calendar. But even in the Gregorian calendar, there's something special about 20.12.2012.

It's one of those dates where the digits create interesting patterns. It also comes at the end of 13 years that have been astonishingly fertile for such numerologically "magic" dates. The rest of the century is going to be a desert by comparison.

Dates can be aesthetically attractive because they repeat a number several times (eg 12.12.12) or contain a string of successive numbers (eg 10.11.12) or because they are palindromes (eg 01.1.10), where you get the same date if you run the numbers backwards.

The beauty of these numbers is in the eye of the beholder. There can be no consensus over what constitutes a date that has numerological significance. But one way of shedding light on the situation is to look at different formats.

First up is the series that runs from 1.1.1 to 2.2.2 and all the way up to 12.12.12. There are only 12 members of this series because there are only 12 months in the year. This feature of the Gregorian Calendar is the main reason why the magic number boom is about to end. We will have to wait 88 years, until 1 January 2101, before we get the next one.

With three members of this series, it is also possible to add a time of day to make the date even more magical: 10.10.10 10.10am (or pm); 11.11.11 11.11am; and 12.12.12,12.12am. The middle one – containing 10 1s in a row – is exceptional.

Next, comes the series that starts with 1.1.11 and ends with 9.9.99. There are nine members in this series, one every decade. The next one is just over nine years away.

Then we have 11.1.11 and 22.2.22. There are just two members of this series because of another feature of the Gregorian calendar: no month has more than 31 days, so you can't get 33.3.33. The next member of this series is nine years away – and then emptiness.

Where you put the dots also matters. 1.11.1, 11.11.1, 1.11.11 are all beauties. But there are, sadly, no more of this type until the next century.

There are 12 dates in the series of which 20.12.2012 is a member – using the European convention that puts the day before the month rather than the American convention that reverses the order. Others include 20.01.2001, 20.02.2002, and 20.09.2009. The last in this series in this century is 20.12.2012. We have to wait 88 years until 21.01.2101 for the next one.

And then there are the palindromes: 01.1.10, 02.2.20 and the rest up to 09.9.90 are really beautiful. The second member of the series can also be written as 02.02.2020 – another great palindrome. Given this double dose of magic, it is worth putting a reminder in the diary for 2 February 2020.

22.02.2022 is another good palindrome, the only member of its series – unless you want to go back more than 900 years to when Henry I was king of England. It too is magical twice over – as February 22 2022 can also be written as 22.2.22.

Then there are dates that contain a string of successive numbers. These include the series: 1.2.3, 2.3.4, and 5.6.7 … The best three, which I count as magical, are: 1.2.3, 10.11.12 and 11.12.13. Set your watch to a quarter past two on 11 December next year: 11.12.13 14.15pm. It's the last really magical number of this decade.

Below is an appendix that lists all the numbers I think make the grade. I reckon there are a total of 68 magical dates in the 21st century, using the convention that the century began on 1 January 2000 rather than 1 January 2001. By the end of 20.12.2012, 43 of these will have passed – an average of just over three a year. There are only 25 left in the next 87 years.

What this means is that the incidence of magic number dates so far this century has been 12 times greater than it will be in the remainder of the century. Unless one is superstitious, there is nothing much one can do with a magic number date apart from admire its beauty. But that's not to sniffed at. Let's cherish 20.12.2012. It's almost the end of an era.